Properties

Label 2.1024.aep_igv
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 119 x + 5585 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0927408016178$, $\pm0.142452920825$
Angle rank:  $2$ (numerical)
Number field:  4.0.43810377.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 932187 1096379621619 1152860430795375168 1208925411936230958208227 1267650638364759142827132988347 1329227998444099071349442280325050624 1393796575025937399348226633156000095509931 1461501637335141232057508077354321241514279023043 1532495540866019570131944297348896009363621603820818496 1606938044258993726602257953101113222574097990438324594740659

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045586 1073684943 1099511256994 1125899940714666 1152921506913320735 1180591620817169298426 1208925819618135025755970 1237940039285485863028960239 1267650600228232123903252170386

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.43810377.1.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.ep_igv$2$(not in LMFDB)